On the automorphisms of generalized algebraic geometry codes

The article delves into the intricate world of generalized algebraic geometry codes (GAG codes), an extension of the classical algebraic geometry codes (AG codes) introduced by Goppa. It focuses on the challenging task of determining the automorphism groups of these codes, which are crucial for understanding their structure and decoding algorithms. The study generalizes previous results by Spera and Picone, showing how certain subgroups of the automorphism group of a GAG code can be embedded into the code's automorphism group under specific conditions. In the case of rational function fields, the article demonstrates that these subgroups can be isomorphic to the automorphism group, providing a significant advancement in the field. The research is particularly notable for its detailed exploration of the relationship between the automorphism groups of GAG codes and their corresponding function fields, offering valuable insights that could lead to further breakthroughs in coding theory.